An earth model of a geological volume of interest represents one or more characteristics of that volume of interest such as spatial structure and compositional properties. Various compositions can include different types of rocks, which can display differing seismic wave propagation velocities. Adjacent geological bodies (e.g., layers) having significant velocity differences can form interfaces known as geological surfaces or horizons. Such surfaces can have very complex shapes, and can result, for example, in reflection and refraction of propagating seismic energy that impinges those surfaces.
For seismic imaging and modeling such as that which includes high-frequency ray approximation, large velocity contrast and complex geological surfaces can make ray energy diffract or turn in an incoherent manner. This can introduce incoherent stacking in an imaging step. Traditionally, processing is applied on a velocity field to reduce velocity contrast at a surface. The smoothness of a surface can be difficult to control. One conventional approach for surface smoothing includes smoothing positional values (e.g., depth values) of a given surface. Since spatial location of a surface changes with this approach, undesired distortions in travel time, phase, and amplitudes can be introduced.